One issue and one question:

First, the question: how does it work adding friends on the Wii when you're hacked? I've read before that I should keep all forms of automatic updating turned off, however, I need to turn WiiConnect24 on to add friends. Can someone make me feel better about turning it on, or maybe a workaround for adding friends? Thanks in advance.

Secondly, Little King's Story and Just Dance 1 are giving me the "black screen of missing IOS" (at least I think that's the problem), and I want to fix this problem and avoid having it with any other games I might be purchasing in the near future. Is there just some magical pack of IOSs out there that I can install all at once to avoid missing one at a later date? Or, is that dangerous and a brickworthy choice? Should I post a system check?

1. Wiiconnect24 will not ruin your softmod, I have it on all the time. Just don't accept any messages that pop up saying "you need to update your system menu" and you'll be fine. Add friends as you normally would - this is how I have added friends.

2. Try installing the d2x cIOS pack - this is known to make a lot of games work. I'll try to post a link in a few moments.

With priiloader set to block disc and online updates, if you click yes it will give an error. So you are safe as long as those 2 hacks are enabled.

Your system check looks fine. I do not see anything missing. (Can update to d2x8, but what you have should work)
What loader are you using? I assume you are loading from USB, since your drive date indicates you cannot load from backup disc.
Make sure you have the latest version of your USB loader. I use the latest WiiFlow and it picks the correct cIOS to load the game for me. Great for when the kids try and play a troublesome game.

Could be that those games are bad dumps. Try and delete them and rerip from the original disc.